Results on infinite-dimensional topology and applications to the structure of the critical set of nonlinear Sturm--Liouville operators

DOI10.1016/S0022-0396(02)00095-5zbMath1025.34023arXivmath/0107197OpenAlexW2138539014MaRDI QIDQ1869776

Dan Burghelea, Nicolau C. Saldanha, Carlos Tomei

Publication date: 28 April 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0107197

zbMATH Keywords

changes of variablesSturm-Liouville operatorcontractibilitycritical set as union of parallel hyperplanesnonlinear infinite-dimensional manifolds

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Sturm-Liouville theory (34B24) Nonlinear ordinary differential operators (34L30) Homotopy and topological questions for infinite-dimensional manifolds (58B05) Infinite-dimensional manifolds (46T05)

Related Items (7)

Stratification of spaces of locally convex curves by itineraries ⋮ Results on the homotopy type of the spaces of locally convex curves on $\mathbb{S}^3$ ⋮ Spaces of curves with constrained curvature on hyperbolic surfaces ⋮ ON THE COMPONENTS OF SPACES OF CURVES ON THE 2-SPHERE WITH GEODESIC CURVATURE IN A PRESCRIBED INTERVAL ⋮ The topology of the monodromy map of a second order ODE ⋮ The geometry of the critical set of nonlinear periodic Sturm-Liouville operators ⋮ The homotopy type of spaces of locally convex curves in the sphere

Cites Work

• Morin singularities and global geometry in a class of ordinary differential operators
• On the inversion of some differentiable mappings with singularities between Banach spaces
• The homotopy type of the unitary group of Hilbert space
• Hilbert manifolds
• Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type
• Diffeomorphisms for Hilbert manifolds and handle decomposition
• Regular level sets of averages of Nemyteskiǐ operators are contractible
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